Because you wouldn't honestly get a rat as a pet and feed it until it was big enough to reach your knee on its hind legs. Let alone try and dye its fur yellow and tell people it's supposed to be Pikachu.

Dogs are generally reserved for Vulpix, Ninetails, Growlithe, (insert further examples of dog-types they've been inserting over the years I have not paid attention to). Cats (at the kitten stage in particular) generally stay still long enough to get the color right and work better towards Pikachu's image with their tongues inside their mouths.

Then why not use a rodent?
It's much closer to pikachu in all ways.
Based on this, I imagine the creator of that gif (or video) to lack information or being like "OMG!! I'M SUCH A NERD!! XDDDDdDD;))))))))"

So you're saying you have actual photos of rats that could work with shopped colors. That's what you're saying, right. Because I still don't see how applying that to a rat would make it work any better. I mean, feel free to prove me wrong by finding such a picture and doing the same, by all means. For the moment, I fail to see how you take so much offense to someone posting a gif of a cat shopped to look like a Pokemon on content involving Pokemon.

In the Pokemon games, the ability Sandstorm effects all types by dealing out damage at the end of both Pokemon's turn except to Pokemon of certain types: Ground, steel, or ground, and Sudowoodo is a Rock type. So, in the games, he wouldn't be effected by the effects of sandstorm, even if it doesn't make much sense.

Unevolved Poke'mon don't have any automatic abilities that affect the weather. Tyranitar creates a sandstorm as soon as it starts battle. You can't stop it from happening and you cant choose it as an ability.